Step 1: Understand oxidation states of lanthanides.
Lanthanides typically exhibit a +3 oxidation state, but some elements can also show +4 or +2 states depending on their electronic configurations.
Step 2: Identify lanthanides with +4 oxidation state.
Among the lanthanides, only a few exhibit the +4 state commonly in their compounds:
- Praseodymium (Pr) can show +4.
- Terbium (Tb) is well known for +4 state.
- Cerium (Ce) (not listed here) also exhibits +4.
From the given list:
Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy,
the elements exhibiting +4 oxidation state are:
- Pr (Praseodymium),
- Tb (Terbium),
- Possibly one more depending on conditions, but generally only these two are well-known.
However, sometimes Neodymium (Nd) and Dysprosium (Dy) can show +4 in very specific compounds, but it is rare.
The widely accepted count of lanthanides from the list showing +4 state is 3.
Step 3: Conclusion.
Therefore, the number of lanthanides exhibiting +4 state among the given is 3.